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Thermodynamically consistent continuum theory of magnetic particles in high-gradient fields

Marko Tesanovic1,*,†, Daniel M. Markiewitz2,*, Marcus L. Popp1, Martin Z. Bazant2,3, and Sonja Berensmeier1,4

  • *These authors contributed equally to this work.
  • †Contact author: m.tesanovic@tum.de
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Phys. Rev. Fluids 11, 054302 – Published 11 May, 2026

DOI: https://doi.org/10.1103/9vzx-5dyv

Abstract

Magnetic particles underpin a broad range of technologies, from water purification and mineral processing to bioseparations and targeted drug delivery. The dynamics of magnetic particles in high-gradient magnetic fields—encompassing both their transport and eventual capture—arise from the coupled interplay of field-driven drift, fluid advection, and particle-field feedback. These processes remain poorly captured by existing models relying on empirical closures or discrete particle tracking. Here we present a thermodynamically consistent continuum theory for collective magnetic particle transport and capture in high-gradient fields. The framework derives from a free-energy functional that couples magnetic energy, entropic mixing, and steric interactions, yielding a concentration-dependent susceptibility via homogenization theory. The resulting equations unify magnetism, mass transport, and momentum balances without ad hoc shut-off criteria, allowing field shielding, anisotropic deposition, and boundary-layer confinement to emerge naturally. Simulations predict canonical capture morphologies—axially aligned plumes, crescent-shaped deposits, and nonlinear shielding—across field strengths and flow regimes, consistent with trends reported in prior experimental and modeling studies. By organizing captured particle mass data into a dimensionless phase diagram based on the Mason number, we reveal three distinct regimes—thermodynamically controlled, transitional, and dynamically controlled. This perspective provides a predictive platform for in silico optimization and extension to 3D geometries, and informing digital twin development for industrial-scale high-gradient magnetic separation processes.

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Phys. Rev. Fluids 11, 054302– Published 11 May, 2026
  • Received 6 November 2025
  • Accepted 10 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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